In the manufacturing industry, like paper, metal, textile and chemical industry, the production process consists of several production stages with corresponding half finished products or end-products.
In many industries producing flat end-products, e.g. paper, steel and other metals, flat-sheet chemicals (e.g. polymers) and film industries, one of the final processing steps is cutting, where a wound up product (reel, coil etc) is cut into smaller products. This is done using special knives and suitable winding systems. What it basically means in practice is that a larger unit (intermediate) will be divided into smaller units (intermediate or end-product), after which further processing or packaging takes place. The end products can be wound up in rolls, machine direction cutting, or cut into sheets, machine and cross direction cutting.
One of the main reasons for postponing the cutting step towards the end of the production is that this allows the simultaneous processing of larger quantities and the design of more generic production equipment that do not depend on certain individual end-product dimensions. Determining a cutting plan faces the following difficulties: How to match the product dimensions required by the customers to those of the equipment and how to group end customer products according to their material property requirements. This problem is referred to as the trim-loss problem or cutting stock problem.
The cutting process can include several subsequent cutting phases. The rolls may also be coated or otherwise processed during the cutting process. The current trim optimization methods have been able to solve only one or two subsequent cutting phases simultaneously. There have also been limitations in considering grade changes, like coating, during the cutting process. Due to the limitations of the existing methods, the trim scheduling has been a step-wise process in the cases with more than two cutting phases and/or grade changes during the cutting process.
The classical trim-loss problem and most work done thereafter are based on the work by Gilmore and Gomory (Gilmore, P. C. and Gomory, R. E. (1961). A linear programming approach to the cutting stock problem, Part I. Operations Research, 9, pp. 849-859). This approach does not take into account the geometrical position of each end-customer product but rather evaluates patterns only through the number of occurrences of product in a pattern.